How to determine the probability of an "existence" question
A human has an abstract concept of numbers in mind. So 456 is a unique entity which is by definition unlike any other number because that are other unique entities. If you give ∃x ∈ ℕ: x==123 to your system it could check the property of natural numbers by counting from 0 to 123 to conclude that the statement is true. A human does it in another way. A human would "see" that it is a natural number because it has no decimal point. Because of the concept of natural numbers the statement is immediately clear. To get a faster result here the machine could check just the decimal point.

In your second case you have to apply the commutative property of addition and you are done because the syntax is equal then.

The second problem is more syntactic while the first is semantic. Your machine may "know" the commutative property of addition but not the concept of natural numbers. Therefore, it has to count.